Relating Binding Energy and Scattering Length of Cold Hybrid Ion‐Atom Systems

Abstract

AbstractThe universal properties of the loosely bound vibrational states of cold hybrid ion‐atom systems are probed using a “scaling” approach. This approach is based on the use of numerical relations (a versus Dlast) between the binding energy (Dlast) of the highest vibrational state and the s‐wave scattering length (a) obtained by solving the appropriate Schrödinger equations with scaled interaction potentials. The actual probing is accomplished by evaluating the “a versus Dlast” relations for 6Li and 7Li in the ground electronic state using a set of ab initio potential energy curves from the literature. Although these curves provide strongly differing values of a and Dlast, the corresponding “a versus Dlast” relations closely coincide, thus enabling an accurate determination of scattering lengths directly from experimental binding energies and vice versa.